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研究了自动微分技术在直接配点法中的应用,将其与内点非线性规划算法相结合,用于求解配点法转化得到的非线性规划问题。采用前向自动微分模式,利用ADOL-C实现了基于算子重载的自动微分计算;为验证算法的性能,以经典的航天飞机再入轨迹优化问题为例,针对三种直接配点格式,比较了自动微分法和有限差分法用于微分计算的性能。研究结果表明,自动微分可以提高微分信息计算的精度和效率,进而提高非线性规划算法的稳定性和收敛速度。
The application of automatic differential technique in direct matching point method is studied. Combining with the interior point nonlinear programming algorithm, this method is used to solve the nonlinear programming problem transformed by the collocation point method. Adopting the forward automatic differential mode, automatic differential computation based on operator overloading is implemented by using ADOL-C. In order to verify the performance of the algorithm, taking classic shuttle reentry trajectory optimization problem as an example, The performance of differential calculus and finite difference calculus for differential calculus The results show that automatic differentiation can improve the accuracy and efficiency of differential information calculation, and then improve the stability and convergence speed of nonlinear programming.